RF Speaker Cables: Bi-wired!

DonH50

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In this second installment on RF and speaker cables we’ll look at bi-wiring. There are those who contend using separate wires for the HF and LF drivers improves sound by minimizing interaction at the speaker terminals, moving it to the amplifier’s output terminals. Since the impedance is lower right at the amplifier outputs (versus at the other end of the cable) any electrical coupling is reduced. For the record, aside from the possible benefit of doubled wires, I do not subscribe to the audibility of bi-wiring, but it makes for an interesting thread. Disclaimer: as usual, because I do not hear anything, does not mean you will not.

First, I set up an ideal speaker with a simple first-order crossover network. With 8-ohm drivers (modeled by pure 8-ohm resistors), a 1.273 mH inductor is in series with the “woofer” and 19.894 uF capacitor in series with the “tweeter” provide a 1 kHz crossover. The crossover frequency is not terribly important for illustrating the effect of bi-wiring, so 1 kHz is just a convenient choice.

Figure 1 shows the frequency response with an 8-ohm speaker cable. The overall response (top light blue line) is perfectly flat, and the crossover frequency to the woofer and tweeter is 1 kHz as designed.

fig1bw_rev1..jpg
Figure 1: Crossover frequency response.​

Figure 2 shows the response into the speaker using a single 8-ohm wire. The amplifier’s output and speaker’s input are essentially the same (with the expected time delay, barely visible at this scale). Recall, or realize, that an inductor will reject high frequencies while a capacitor rejects low frequencies. The inductor looks like an open to a high-frequency signal, and the capacitor looks like a short. With the step input signal used, the tweeter responds immediately, then falling as the capacitor charges since as the pulse stays high it looks more and more like a d.c. signal. The inductor blocks the high-frequency step from the woofer and thus its voltage rises only very gradually.

fig2bw_rev1..jpg
Figure 2: Single 8-ohm speaker wire.​

Now what happens if bi-wire and we look at the speaker terminals? See Figure 3… The woofer inputs with 8-ohm and 93-ohm (Monster cable) lines are in the top plot, and the tweeter inputs are in the bottom plot. The tweeter input response looks very similar to that of the single wire and simple load of the previous thread, with the 8-ohm cable providing an immediate step and the Monster Cable’s line mismatch yielding reflections that result in a slower, “stepped” rise time. The capacitor is essentially a short circuit as discussed earlier and so initially the system is virtually identical to the test case in the previous speaker cable thread.

fig3bw_rev1..jpg
Figure 3. Bi-wiring response.​

The woofer input is much more interesting. Since the inductor is an open to high-frequencies, the initial (fast) step “sees” an open circuit, causing a reflection that doubles the signal level at the terminals. The reflection travels back to the amp, is inverted and reflected by the zero-ohm (amp) source, travels back to the speaker terminal, and the cycle repeats. A little more energy goes into the woofer as time goes on, and eventually will settle to its final value. The lossy Monster Cable line (green) actually appears to settle a little faster, primarily due to band-limiting and the resistive loss.

So, bi-wiring does affect the voltage at the speaker terminals, though ideally does not affect the actual speaker’s response. The extra reflections introduced could make it tougher on the amplifier, though we must remember a real amp will have higher output impedance (especially at high frequency) and thus damp the ringing more quickly. While these are the expected waveforms from an RF engineering perspective, I am guessing it is news to many audiophiles…

FYI - Don
 

Ron Party

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Seriously. What an asset you are to this forum. Does your trumpet playing compare to the level of expertise you repeatedly demonstrate in our forum?:)
 

DonH50

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Thanks guys! I must note that there are many engineers that could do the same, much as it loathes me to admit; I am by no means unique. A lot know a lot more about audio circuits than I, too (high-speed design tends toward much simpler circuits, the trade for speed). And Ron, I do OK on trumpet (i.e. they keep asking me back), but I learned way too young that whilst I was a very good trumpet player, great trumpet players were barely making it, and mediocre engineers were doing just fine! :) For me, trumpet playing is a great hobby, but I don't think I could make a living at it. Did make a few bucks subbing on the lead book in a big band couple of weeks ago, enough for a few new CDs. Orchestra rehearsals start soon (www.pikespeakphil.org) so I need to haul out all the horns I have neglected all summer and get re-acquainted.
 

Speedskater

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I think that we should point out that there are no real world 8 Ohm characteristic impedance speaker cables at audio frequencies.
The one exception is the Dynaudio Ocos.

Typical speaker cables have a 20Hz characteristic impedance of from 1000 to 10,000 Ohms and a 20kHz characteristic impedance from 100 to 500 Ohms.
 

DonH50

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Good point. Mogami claims 8 ohms, and I have heard of others but none come immediately to mind, but they are certainly not the norm. My choice was to show what happens with a "perfect" system, not to imply you could get one. Even if you could, I have yet to find a speaker that represents a perfect wideband 8-ohm impedance so IMO getting an 8-ohm cable is moot.

There are things going on that make the T-line characteristic impedance assumptions fall apart at very low (and very, very high, but that does not matter) frequencies, including the added series R (see the earlier thread for the equation). I did not get into that, and probably won't as I am not very familiar with LF transmission lines.
 

DonH50

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Here's an interesting set of plots. I decided to make my amp model more "real" by increasing the resistance to realize an effective damping factor (8 ohms) of 100 at d.c., dropping to ~10 around 10 kHz (inductive output). I used the Monster Cable model and simulated regular and bi-wired cases as before. Here are the before and after plots:
20110805_real_amp1&.JPG
The top two plots are the same as before, showing the single (top) and bi-wire (second from top) cases. The next plot, third from top, is the same as the top but now with my new "more real" amp model. The light blue line is the tweeter's input, very similar to the top plot but with slower rise (due to the amp's inductive output) and the woofer's input (bottom green line) is nearly identical (since the inductance does not affect LF as much). The darker blue line is the amplifier's output terminal and is essentially invisible in the top plot due to it's ideal'ish fast rise time. So, the "real" amp has significantly slowed the amplifier's output, and added ringing and settling artifacts.

The bottom plot shows the bi-wire case with the "real" amp. The red line shows the woofer's input; notice it is now much more damped and settles much more quickly with the real amp. Again, the actual woofer's output (bottom line) is practically the same. The tweeter' input is very similar to the plot above, but close inspection reveals a little more ringing compared to the single-wire case. Finally, the amp's output (darker blue, almost hidden in the woofer's input ringing) is actually higher in amplitude than with a single wire, and the ringing takes longer to settle.

Frankly, while the speed with which all these waveforms settle makes their audibility questionable, just looking at the amplifier's output and speaker's inputs makes me want to not bi-wire!

FYI - Don
 
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j_n

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Interesting modelling, thanks Don.

I would not be worried about the system's response to high speed transitions, as they are only a modelling tool for t line analysis. Yes, the analysis shows some really interesting spikes and all, but in real life there is no energy at those frequencies available to stimulate such activity.

The analysis using fast transition steps is best used conceptually. The overall system response after analysis needs to be filtered to remove the hf content.

Do you have the ability to model a woof and tweet where each has impedance dips down into the 1 ohm area and peaks up in the 100 ohm? Then compare an 8 ohm cable vs a 100?

Cheers, jn
 

DonH50

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Hey, you started it! :)

I was more concerned about the envelope than the actual HF content; my last comment puts us in agreement, I think.

As for more complex models, "ability" yes, time no... Deriving a model from observed impedance plots (e.g. from a review) can be tricky and I do not have an easy way to do that. (There are SW tools, but I do not have any now.) I thought about it some but ran out of time. These little articles tend to be the work of a few hours here and there over a weekend; they very often lead to me spending way more time tha nI should, and still leave a host of unanswered questions and paths for further exploration. Maybe in a few decades, or centuries, when I can afford to retire...
 

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